Question

19 multiple choice 1 point a cylinder has a volume of 33 cubic inches. what is the volume of a cone with the same radius and height? 33 cubic inches 44 cubic inches 99 cubic inches 11 cubic inches 0 21

Explanation:

Step1: Recall the volume formulas

The volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\), and the volume formula of a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\).

Step2: Relate the volumes

If the cone and the cylinder have the same radius \(r\) and height \(h\), then \(V_{cone}=\frac{1}{3}V_{cylinder}\).
Given \(V_{cylinder} = 33\) cubic inches.
Substitute \(V_{cylinder}\) into the formula: \(V_{cone}=\frac{1}{3}\times33\).

Step3: Calculate the volume of the cone

\(V_{cone}=\frac{33}{3}=11\) cubic inches.

Answer:

11 cubic inches